Minimize steps to make Array elements equal by deleting adjacent pair and inserting bitwise OR

Given an array arr[], consisting of N integers, the task is to find the minimum number of moves required to make all numbers in the resulting array equal. In one move,  

• Take two adjacent numbers arr[i] and arr[i+1], and delete them. 
• Insert the bitwise OR of arr[i] and arr[i+1] at the deleted position. 

Examples:

Input: arr[] = {1, 1, 1, 0, 1}
Output: 1
Explanation: After OR operation on arr[2] and arr[3] we get, 1 | 0 = 1. 
Since, array arr[] becomes {1, 1, 1, 1} and here all elements are equal. 
Thus, it takes only 1 move to make all the numbers equal.

Input: arr[] = {1, 2, 3}
Output: 1
Explanation: After OR operation on arr[0] and arr[1] we get, 1 | 2 = 3. 
Now, array arr[] becomes {3, 3} and here both elements are equal. 
Thus, it takes only 1 move to make all the numbers equal.

Approach: The problem can be solved based on the following observation of bitwise properties:

It is known that x | x = x, [where ‘|’ means bitwise OR]. 

Lets say that the array has all the elements as X at the end and total M elements.
Based on this we can assume that there were M subarrays such that bitwise OR of the subarray elements are X.

The closer the value of M to N, the less operations are done.
So the task reduces to find the maximum number of subarray such that they have bitwise OR = X

If there are M such subarrays, then the number of operations performed = N – M (because in each step size reduces by 1)

Follow the below steps to solve the problem:

• Find bitwise OR of all array elements and store it (say Total_Or).
• Initialize a variable (say Group = 0) to count how many subarrays have the OR value of Total_Or.
• Run a loop in the array from i = 0 to N:
  • Calculate the bitwise OR of the elements (say Current_Or).
  • If Current_Or is the same as Total_Or, Increment Group by 1 and set Current_Or = 0;
• After executing the loop, return N – Group.

Below is the implementation of the above approach:

C++

// C++ code to implement the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to return minimum number of moves
int findMinMoves(int* arr, int n)
{
    // Initialize the variables
    int Total_Or = 0;
    int Current_Or = 0;
    int Group = 0;

    // Find or of all array elements
    for (int i = 0; i < n; i++) {
        Total_Or |= arr[i];
    }

    // Find number of groups forming or
    // equal to Total_Or
    for (int i = 0; i < n; i++) {
        Current_Or |= arr[i];

        // If Current_Or = Total_Or,
        // increment Group by 1
        if (Current_Or == Total_Or) {
            Group++;

            // Reset Current_Or
            Current_Or = 0;
        }
    }

    // Return minimum number of moves
    return n - Group;
}

// Driver Code
int main()
{
    int arr[] = { 1, 1, 1, 0, 1 };
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    cout << findMinMoves(arr, N);
    return 0;
}

Java

/*package whatever //do not write package name here */
import java.io.*;

class GFG
{

  // Java code to implement the above approach

  // Function to return minimum number of moves
  static int findMinMoves(int arr[], int n)
  {
    // Initialize the variables
    int Total_Or = 0;
    int Current_Or = 0;
    int Group = 0;

    // Find or of all array elements
    for (int i = 0; i < n; i++) {
      Total_Or |= arr[i];
    }

    // Find number of groups forming or
    // equal to Total_Or
    for (int i = 0; i < n; i++) {
      Current_Or |= arr[i];

      // If Current_Or = Total_Or,
      // increment Group by 1
      if (Current_Or == Total_Or) {
        Group++;

        // Reset Current_Or
        Current_Or = 0;
      }
    }

    // Return minimum number of moves
    return n - Group;
  }

  // Driver Code
  public static void main(String args[])
  {
    int arr[] = { 1, 1, 1, 0, 1 };
    int N = arr.length;

    // Function call
    System.out.println(findMinMoves(arr, N));
  }
}

// This code is contributed by shinjanpatra

Python3

# Python3 code to implement the above approach
# Function to return minimum number of moves
def findMinMoves(arr,n):

    # Initialize the variables
    Total_Or = 0;
    Current_Or = 0;
    Group = 0;

    # Find or of all array elements
    for i in range(0,n):
        Total_Or = Total_Or|arr[i]

    # Find number of groups forming or
    # equal to Total_Or
    for i in range(0,n):
        Current_Or |= arr[i]

        # If Current_Or = Total_Or,
        # increment Group by 1
        if (Current_Or == Total_Or):
            Group=Group+1

            # Reset Current_Or
            Current_Or = 0
    # Return minimum number of moves
    return n - Group

# Driver Code
N = 5
arr = [ 1, 1, 1, 0, 1 ]

# Function call
print(findMinMoves(arr, N))

# This code is contributed by akashish__

C#

using System;

public class GFG{

  // Function to return minimum number of moves
  static int findMinMoves(int[] arr, int n)
  {

    // Initialize the variables
    int Total_Or = 0;
    int Current_Or = 0;
    int Group = 0;

    // Find or of all array elements
    for (int i = 0; i < n; i++) {
      Total_Or |= arr[i];
    }

    // Find number of groups forming or
    // equal to Total_Or
    for (int i = 0; i < n; i++) {
      Current_Or |= arr[i];

      // If Current_Or = Total_Or,
      // increment Group by 1
      if (Current_Or == Total_Or) {
        Group++;

        // Reset Current_Or
        Current_Or = 0;
      }
    }

    // Return minimum number of moves
    return n - Group;
  }

  public static void Main ()
  {

    // Code
    int N = 5;
    int[] arr = { 1, 1, 1, 0, 1 };

    // Function call
    int ans = findMinMoves(arr, N);
    Console.WriteLine(ans);
  }
}

// This code is contributed by akashish__

Javascript

<script>
       // JavaScript code for the above approach

       // Function to return minimum number of moves
       function findMinMoves(arr, n) {
           // Initialize the variables
           let Total_Or = 0;
           let Current_Or = 0;
           let Group = 0;

           // Find or of all array elements
           for (let i = 0; i < n; i++) {
               Total_Or |= arr[i];
           }

           // Find number of groups forming or
           // equal to Total_Or
           for (let i = 0; i < n; i++) {
               Current_Or |= arr[i];

               // If Current_Or = Total_Or,
               // increment Group by 1
               if (Current_Or == Total_Or) {
                   Group++;

                   // Reset Current_Or
                   Current_Or = 0;
               }
           }

           // Return minimum number of moves
           return n - Group;
       }

       // Driver Code

       let arr = [1, 1, 1, 0, 1];
       let N = arr.length;

       // Function call
       document.write(findMinMoves(arr, N));


   // This code is contributed by Potta Lokesh
   </script>

Output

1

Time Complexity: O(N)
Auxiliary Space: O(1)